Finite Group DatabasebetaFinite Group Databasebeta| order | 17488 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C1093 ⋊ C2 |
| Sylow | C1093 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1093 |
| commutator, socle, cosocle | C2×C1093 | C23 |
| Fitting | D4×C1093 | C2 |
| hypercenter | D4 | D1093 |
| hypocenter | C1093 | #41 |
| LCS | G ▷ C2×C1093 ▷ C1093 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8744 |
Polycyclic presentation:
2^4,1093|c^2=d,b^a=bd,e^c=e^10922740 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46854126, #46854128, #46854131, … |
| maximal normal subgroup of | #46854126, #46854128, #46854131, … |
| maximal quotient of | #46854063, #46854065, #46854067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17488, 39);